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x^2<x
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16 Mar 2022, 02:00
16 Mar 2022, 02:00
Expert Reply
00:00
Question Stats:
53% (00:38) correct
46% (00:32) wrong based on 26 sessions
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\(x^2<x\)
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
x |
0 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Re: x^2<x
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16 Mar 2022, 11:04
16 Mar 2022, 11:04
1
Carcass wrote:
\(x^2<x\)
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
x |
0 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
To fulfill the condition \(x^2<x\), x have to be like : 0 < x < 1
Hence x is always greater than 0
x^2<x
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16 Mar 2022, 12:07
16 Mar 2022, 12:07
Carcass wrote:
\(x^2<x\)
Quantity A |
Quantity B |
x |
0 |
Alternate approach:
If \(x\) is NONZERO, then \(x^2 =\) POSITIVE.
\(x^2 < x \) implies that x is nonzero, since \(0^2\) is not less than \(0\).
Implication:
Since \(x\) is nonzero, \(x^2 =\) positive, allowing us to divide both sides of \(x^2 < x\) by \(x^2\):
\(\frac{x^2}{x^2} < \frac{x}{x^2}\)
\(1 < \frac{1}{x}\)
\(\frac{1}{x}\) is greater than 1 and thus must be positive.
Implication:
\(x\) itself must be positive.
Quantity A is greater.
Show: ::
A
